51 ideas
6267 | A culture needs to admit that knowledge is more extensive than just 'science' [Putnam] |
6272 | 'True' and 'refers' cannot be made scientically precise, but are fundamental to science [Putnam] |
6276 | 'The rug is green' might be warrantedly assertible even though the rug is not green [Putnam] |
6266 | We need the correspondence theory of truth to understand language and science [Putnam] |
6277 | Correspondence between concepts and unconceptualised reality is impossible [Putnam] |
6264 | In Tarski's definition, you understand 'true' if you accept the notions of the object language [Putnam] |
6265 | Tarski has given a correct account of the formal logic of 'true', but there is more to the concept [Putnam] |
6269 | Only Tarski has found a way to define 'true' [Putnam] |
14273 | Conditional Proof is only valid if we accept the truth-functional reading of 'if' [Edgington] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
6280 | Realism is a theory, which explains the convergence of science and the success of language [Putnam] |
14281 | A thing works like formal probability if all the options sum to 100% [Edgington] |
14284 | Conclusion improbability can't exceed summed premise improbability in valid arguments [Edgington] |
14270 | Simple indicatives about past, present or future do seem to form a single semantic kind [Edgington] |
14269 | Maybe forward-looking indicatives are best classed with the subjunctives [Edgington] |
14275 | Truth-function problems don't show up in mathematics [Edgington] |
14274 | Inferring conditionals from disjunctions or negated conjunctions gives support to truth-functionalism [Edgington] |
14276 | The truth-functional view makes conditionals with unlikely antecedents likely to be true [Edgington] |
14290 | Doctor:'If patient still alive, change dressing'; Nurse:'Either dead patient, or change dressing'; kills patient! [Edgington] |
14271 | Non-truth-functionalist say 'If A,B' is false if A is T and B is F, but deny that is always true for TT,FT and FF [Edgington] |
14272 | I say "If you touch that wire you'll get a shock"; you don't touch it. How can that make the conditional true? [Edgington] |
14282 | On the supposition view, believe if A,B to the extent that A&B is nearly as likely as A [Edgington] |
14278 | Truth-functionalists support some conditionals which we assert, but should not actually believe [Edgington] |
14287 | Does 'If A,B' say something different in each context, because of the possibiites there? [Edgington] |
6284 | If a tautology is immune from revision, why would that make it true? [Putnam] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
6273 | Knowledge depends on believing others, which must be innate, as inferences are not strong enough [Putnam] |
6274 | Empathy may not give knowledge, but it can give plausibility or right opinion [Putnam] |
17084 | You can't decide which explanations are good if you don't attend to the interest-relative aspects [Putnam] |
6282 | Theory of meaning presupposes theory of understanding and reference [Putnam] |
6281 | Truth conditions can't explain understanding a sentence, because that in turn needs explanation [Putnam] |
6278 | We should reject the view that truth is prior to meaning [Putnam] |
6271 | How reference is specified is not what reference is [Putnam] |
6268 | The claim that scientific terms are incommensurable can be blocked if scientific terms are not descriptions [Putnam] |
6279 | A private language could work with reference and beliefs, and wouldn't need meaning [Putnam] |
6270 | The correct translation is the one that explains the speaker's behaviour [Putnam] |
6283 | Language maps the world in many ways (because it maps onto other languages in many ways) [Putnam] |
6275 | You can't say 'most speaker's beliefs are true'; in some areas this is not so, and you can't count beliefs [Putnam] |